E-LC04 · Tangency and the position of two intersections
The curve is \(y=x^2-4x+7\). A line through \((0,3)\) has equation \(y=mx+3\).
Form the intersection equation in x and find its discriminant in terms of m.
Find the two tangent lines and their contact points.
Find all m for which the line meets the curve at two distinct points both strictly to the right of the y-axis.
Complete-answer checking, worked solutions and indicative written criteria.
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